<s>
In	O
mathematics	O
,	O
an	O
alternating	B-Algorithm
sign	I-Algorithm
matrix	I-Algorithm
is	O
a	O
square	B-Algorithm
matrix	I-Algorithm
of	O
0s	O
,	O
1s	O
,	O
and	O
−1s	O
such	O
that	O
the	O
sum	O
of	O
each	O
row	O
and	O
column	O
is	O
1	O
and	O
the	O
nonzero	O
entries	O
in	O
each	O
row	O
and	O
column	O
alternate	O
in	O
sign	O
.	O
</s>
<s>
These	O
matrices	O
generalize	O
permutation	B-Algorithm
matrices	I-Algorithm
and	O
arise	O
naturally	O
when	O
using	O
Dodgson	O
condensation	O
to	O
compute	O
a	O
determinant	O
.	O
</s>
<s>
A	O
permutation	B-Algorithm
matrix	I-Algorithm
is	O
an	O
alternating	B-Algorithm
sign	I-Algorithm
matrix	I-Algorithm
,	O
and	O
an	O
alternating	B-Algorithm
sign	I-Algorithm
matrix	I-Algorithm
is	O
a	O
permutation	B-Algorithm
matrix	I-Algorithm
if	O
and	O
only	O
if	O
no	O
entry	O
equals	O
.	O
</s>
